Rejection Region

A rejection region (or critical region)
is the set of all values of the test statistic that cause us to reject the null
hypothesis.

If the test statistic falls into the rejection region, we
reject the null hypothesis in favor of the alternative hypothesis.

If the test statistic falls in the non-rejection region, we
say that we do not have evidence to reject the null hypothesis.

Rejection and Non-rejection Regions

Outcomes that result in the rejection of the null hypothesis
lie in what is termed the rejection region.

So when is the outcome, e.g. a sample mean, so far away from
the population mean that the null hypothesis is rejected? The critical values
are used to divide the means that lead to the rejection of the null hypothesis
from those that do not.

In each direction beyond the critical values lie the
rejection regions. Any sample mean that falls in that region will lead the
business researcher to reject the null hypothesis. Sample means that fall
between the two critical values are close enough to the population mean that
the business researcher will decide not to reject the null hypothesis. These
means are in the non-rejection region.

A Type I error is committed by rejecting a
true null hypothesis.

A Type II error is committed when a business
researcher fails to reject a false null hypothesis.